Recall that a module \(M\)  is called quasi-continuous if \(M\)  is CS and, for any two direct summands \(M_1\) , \(M_2\)  with \(M_1 \cap M_2 = 0\) ,
\(M_1 \oplus M_2\)  is also a direct summand (see [1]}). From [2]},
it follows that a faithful \(R\) -module \(M\)  is weakly IN if and only if \(M\)  is a quasi-continuous \(R\) -module and for any \(f^2=f\in End_R(M)\) ,
there exists \(r\in R\)  such that \(f(x)=rx\)  for any \(x\in M\) . This fact can be extended to the general case as shown in the following characterization
of weakly IN modules.
